The number of publications on mathematical modeling of cancer is growing at an exponential rate, according to PubMed records, provided by the US National Library of Medicine and the National Institutes of Health. Seminal papers have initiated and promoted mathematical modeling of cancer and have helped define the field of mathematical oncology (Norton and Simon in J Natl Cancer Inst 58:1735–1741, 1977; Norton in Can Res 48:7067–7071, 1988; Hahnfeldt et al. in Can Res 59:4770–4775, 1999; Anderson et al. in Comput Math Methods Med 2:129–154, 2000. https://doi.org/10.1080/10273660008833042; Michor et al. in Nature 435:1267–1270, 2005. https://doi.org/10.1038/nature03669; Anderson et al. in Cell 127:905–915, 2006. https://doi.org/10.1016/j.cell.2006.09.042; Benzekry et al. in PLoS Comput Biol 10:e1003800, 2014. https://doi.org/10.1371/journal.pcbi.1003800). Following the introduction of undergraduate and graduate programs in mathematical biology, we have begun to see curricula developing with specific and exclusive focus on mathematical oncology. In 2018, 218 articles on mathematical modeling of cancer were published in various journals, including not only traditional modeling journals like the Bulletin of Mathematical Biology and the Journal of Theoretical Biology, but also publications in renowned science, biology, and cancer journals with tremendous impact in the cancer field (Cell, Cancer Research, Clinical Cancer Research, Cancer Discovery, Scientific Reports, PNAS, PLoS Biology, Nature Communications, eLife, etc). This shows the breadth of cancer models that are being developed for multiple purposes. While some models are phenomenological in nature following a bottom-up approach, other models are more top-down data-driven. Here, we discuss the emerging trend in mathematical oncology publications to predict novel, optimal, sometimes even patient-specific treatments, and propose a convention when to use a model to predict novel treatments and, probably more importantly, when not to.

Intermittent androgen deprivation therapy (IADT) is an attractive treatment for biochemically recurrent prostate cancer (PCa), whereby cycling treatment on and off can reduce cumulative dose and limit toxicities. We simulate prostate-specific antigen (PSA) dynamics, with enrichment of PCa stem-like cell (PCaSC) during treatment as a plausible mechanism of resistance evolution. Simulated PCaSC proliferation patterns correlate with longitudinal serum PSA measurements in 70 PCa patients. Learning dynamics from each treatment cycle in a leave-one-out study, model simulations predict patient-specific evolution of resistance with an overall accuracy of 89% (sensitivity = 73%, specificity = 91%). Previous studies have shown a benefit of concurrent therapies with ADT in both low- and high-volume metastatic hormone-sensitive PCa. Model simulations based on response dynamics from the first IADT cycle identify patients who would benefit from concurrent docetaxel, demonstrating the feasibility and potential value of adaptive clinical trials guided by patient-specific mathematical models of intratumoral evolutionary dynamics.

Abiraterone acetate (AA) has been proven effective for metastatic castration-resistant prostate cancer (mCRPC), and it has been proposed that adaptive AA may reduce toxicity and prolong time to progression, when compared to continuous AA. We developed a simple quantitative model of prostate-specific antigen (PSA) dynamics to evaluate prostate cancer (PCa) stem cell enrichment as a plausible driver of AA treatment resistance. The model incorporated PCa stem cells, non-stem PCa cells and PSA dynamics during adaptive therapy. A leave-one-out analysis was used to calibrate and validate the model against longitudinal PSA data from 16 mCRPC patients receiving adaptive AA in a pilot clinical study. Early PSA treatment response dynamics were used to predict patient response to subsequent treatment. We extended the model to incorporate metastatic burden and also investigated the survival benefit of adding concurrent chemotherapy for patients predicted to become resistant. Model simulations demonstrated PCa stem cell self-renewal as a plausible driver of resistance to adaptive therapy. Evolutionary dynamics from individual treatment cycles combined with metastatic burden measurements predicted patient response with 81% accuracy (specificity=92%, sensitivity=50%). In those patients predicted to progress, simulations of the addition of concurrent chemotherapy suggest a benefit between 1% and 11% reduction in probability of progression when compared to adaptive AA alone. This study developed the first mCRPC patient-specific mathematical model to use early PSA treatment response dynamics to predict subsequent responses to adaptive AA, demonstrating the putative value of integrating mathematical modeling into clinical decision making.

Adaptive therapy with abiraterone acetate (AA), whereby treatment is cycled on and off, has been presented as an alternative to continuous therapy for metastatic castration resistant prostate cancer (mCRPC). It is hypothesized that cycling through treatment allows sensitive cells to competitively suppress resistant cells, thereby increasing the amount of time that treatment is effective. It has been proposed that there exists a subset of patients for whom this competition can be enhanced through slight modifications. Here, we investigate how adaptive AA can be modified to extend time to progression using a simple mathematical model of stem cell, non-stem cell, and prostate-specific antigen (PSA) dynamics. The model is calibrated to longitudinal PSA data from 16 mCRPC patients undergoing adaptive AA in a pilot clinical study at Moffitt Cancer Center. Model parameters are then used to simulate range-bounded adaptive therapy (RBAT) whereby treatment is modulated to maintain PSA levels between pre-determined patient-specific bounds. Model simulations of RBAT are compared to the clinically applied adaptive therapy and show that RBAT can further extend time to progression, while reducing the cumulative dose patients received in 11/16 patients. Simulations also show that the cumulative dose can be reduced by up to 40% under RBAT. Through small modifications to the conventional adaptive therapy design, our study demonstrates that RBAT offers the opportunity to improve patient care, particularly in those patients who do not respond well to conventional adaptive therapy.

Acquiring sufficient data is imperative to accurately predict tumor growth dynamics and effectively treat patients. The aim of this study was to investigate the number of volume measurements necessary to predict breast tumor growth dynamics using the logistic growth model. The model was calibrated to tumor volume data from 18 untreated breast cancer patients using a varying number of measurements interpolated at clinically relevant timepoints with different levels of noise (0–20%). Error-to-model parameters and the data were compared to determine the sufficient number of measurements needed to accurately determine growth dynamics. We found that without noise, three tumor volume measurements are necessary and sufficient to estimate patient-specific model parameters. More measurements were required as the level of noise increased. Estimating the tumor growth dynamics was shown to depend on the tumor growth rate, clinical noise level, and acceptable error of the to-be-determined parameters. Understanding the relationship between these factors provides a metric by which clinicians can determine when sufficient data have been collected to confidently predict patient-specific tumor growth dynamics and recommend appropriate treatment options.

Purpose: Minimally invasive biomarkers have been used as important indicators of treatment response and progression in cancers such as prostate and ovarian. Unfortunately, all biomarkers are not prognostic in all cancer types and are often not routinely collected. Patient-reported outcomes (PRO) provide a non-obtrusive, personalized measure of a patient's quality of life and symptomatology, reported directly from the patient, and are increasingly collected as part of routine care. Previous literature has shown correlations between specific PROs (i.e., insomnia, fatigue) and overall survival. Although promising, these studies often only consider single time points and ignore patient-specific dynamic changes in individual PROs, which might be early predictors of treatment response or progression. Experimental Design: In this study, PRO dynamics were analyzed to determine if they could be used as interradiographic predictors of tumor volume changes among 85 patients with non–small cell lung cancer undergoing immunotherapy. PRO questionnaires and tumor volume scans were completed biweekly and monthly, respectively. Correlation and predictive analysis were conducted to identify specific PROs that could accurately predict patient response. Results: Changes in tumor volume over time were significantly correlated with dizziness (P < 0.005), insomnia (P < 0.05), and fatigue (P < 0.05). In addition, cumulative changes in insomnia could predict progressive disease with a 77% accuracy, on average 45 days prior to the next imaging scan. Conclusions: This study presents the first time that patient-specific PRO dynamics have been considered to predict how individual patients will respond to treatment. This is an important first step in adapting treatment to improve response rates.